From the registry of the birth certificates for this town, year, part, series and numbers indicated above, the results are:
Guiliano (surname) Francesco (1st name on birth act)
son of Giuseppe and Marianna Sabatini born in Onano (VT) on the 11th day of the month of May in the year 1893

I noticed in that arrival manifest on 1909 Francesco Giuliano declared to leave in Italy his mother Sabatina.... but Sabatini was his mother's maiden name!!!
So there is no doubt that the 1909 arrival manifest matches with the birth act.....

I just put together what you were saying about the connection between the birth certificate and the manifest entry. This is the biggest breakthrough we've ever had! To make it even better, I found out that my grandfather listed "Marian Sabatin" as his mother on a social security form.

Now that I have connected him to a town in Italy (Onano), any ideas on how to proceed from here?